Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Percentage Accurate: 94.3% → 97.2%

Time: 26.8s

Alternatives: 23

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 94.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right), c - b, \sqrt{a + t} \cdot \frac{z}{t}\right)\right)}, x\right)} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (fma
   y
   (pow
    (exp 2.0)
    (fma
     (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t)))
     (- c b)
     (* (sqrt (+ a t)) (/ z t))))
   x)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / fma(y, pow(exp(2.0), fma((0.8333333333333334 + (a - (0.6666666666666666 / t))), (c - b), (sqrt((a + t)) * (z / t)))), x);
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / fma(y, (exp(2.0) ^ fma(Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))), Float64(c - b), Float64(sqrt(Float64(a + t)) * Float64(z / t)))), x))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision] + N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Step-by-step derivation

   1. +-commutative 96.1%

      \[\leadsto \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]

   2. fma-def 96.1%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right), c - b, \sqrt{t + a} \cdot \frac{z}{t}\right)\right)}, x\right)}} \]

4. Final simplification 99.2%

   \[\leadsto \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right), c - b, \sqrt{a + t} \cdot \frac{z}{t}\right)\right)}, x\right)} \]

Alternative 2: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\sqrt{a + t} \cdot z}{t} + \left(c - b\right) \cdot \left(\left(0.8333333333333334 + a\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* (sqrt (+ a t)) z) t)
          (* (- c b) (- (+ 0.8333333333333334 a) (/ 2.0 (* t 3.0)))))))
   (if (<= t_1 INFINITY)
     (/ x (+ x (* y (exp (* 2.0 t_1)))))
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((Math.sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((math.sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(sqrt(Float64(a + t)) * z) / t) + Float64(Float64(c - b) * Float64(Float64(0.8333333333333334 + a) - Float64(2.0 / Float64(t * 3.0)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((sqrt((a + t)) * z) / t) + ((c - b) * ((0.8333333333333334 + a) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * N[(N[(0.8333333333333334 + a), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))) < +inf.0

   1. Initial program 99.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   if +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))

   1. Initial program 0.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 67.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sqrt{a + t} \cdot z}{t} + \left(c - b\right) \cdot \left(\left(0.8333333333333334 + a\right) - \frac{2}{t \cdot 3}\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} + \left(c - b\right) \cdot \left(\left(0.8333333333333334 + a\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \end{array} \]

Alternative 3: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)}}\\ \mathbf{if}\;t \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 200000000000:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (+
               (* z (sqrt (/ 1.0 t)))
               (*
                (- c b)
                (+
                 0.8333333333333334
                 (* 0.6666666666666666 (/ -1.0 t))))))))))))
   (if (<= t 2e-284)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
     (if (<= t 1.02e-47)
       t_1
       (if (<= t 200000000000.0)
         (/
          x
          (+
           x
           (*
            y
            (pow
             (exp (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a)))
             (* 2.0 b)))))
         (if (<= t 8e+161)
           t_1
           (/
            x
            (+
             x
             (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	double tmp;
	if (t <= 2e-284) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1.02e-47) {
		tmp = t_1;
	} else if (t <= 200000000000.0) {
		tmp = x / (x + (y * pow(exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else if (t <= 8e+161) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((c - b) * (0.8333333333333334d0 + (0.6666666666666666d0 * ((-1.0d0) / t)))))))))
    if (t <= 2d-284) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 1.02d-47) then
        tmp = t_1
    else if (t <= 200000000000.0d0) then
        tmp = x / (x + (y * (exp(((0.6666666666666666d0 / t) + ((-0.8333333333333334d0) - a))) ** (2.0d0 * b))))
    else if (t <= 8d+161) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	double tmp;
	if (t <= 2e-284) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1.02e-47) {
		tmp = t_1;
	} else if (t <= 200000000000.0) {
		tmp = x / (x + (y * Math.pow(Math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else if (t <= 8e+161) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))))
	tmp = 0
	if t <= 2e-284:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 1.02e-47:
		tmp = t_1
	elif t <= 200000000000.0:
		tmp = x / (x + (y * math.pow(math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))))
	elif t <= 8e+161:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(c - b) * Float64(0.8333333333333334 + Float64(0.6666666666666666 * Float64(-1.0 / t))))))))))
	tmp = 0.0
	if (t <= 2e-284)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 1.02e-47)
		tmp = t_1;
	elseif (t <= 200000000000.0)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))) ^ Float64(2.0 * b)))));
	elseif (t <= 8e+161)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	tmp = 0.0;
	if (t <= 2e-284)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 1.02e-47)
		tmp = t_1;
	elseif (t <= 200000000000.0)
		tmp = x / (x + (y * (exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))) ^ (2.0 * b))));
	elseif (t <= 8e+161)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + N[(0.6666666666666666 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2e-284], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-47], t$95$1, If[LessEqual[t, 200000000000.0], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(2.0 * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+161], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 2.00000000000000007e-284

   1. Initial program 88.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 90.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   if 2.00000000000000007e-284 < t < 1.02000000000000002e-47 or 2e11 < t < 8.0000000000000003e161

   1. Initial program 99.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around 0 94.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\sqrt{\frac{1}{t}} \cdot z - \left(0.8333333333333334 - 0.6666666666666666 \cdot \frac{1}{t}\right) \cdot \left(b - c\right)\right)}}} \]

   if 1.02000000000000002e-47 < t < 2e11

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 70.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 70.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   5. Taylor expanded in y around 0 70.4%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   6. Step-by-step derivation

      1. associate-*r* 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

      2. associate--r+ 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      3. sub-neg 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \left(-a\right)\right)}}} \]

      4. mul-1-neg 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{-1 \cdot a}\right)}} \]

      5. +-commutative 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      6. associate--l+ 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      7. associate-*r* 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(b \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)\right)}}} \]

      8. associate-*r* 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      9. associate--l+ 70.4%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      10. +-commutative 70.4%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + -1 \cdot a\right)}}} \]

      11. mul-1-neg 70.4%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{\left(-a\right)}\right)}} \]

      12. sub-neg 70.4%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      13. associate--r+ 70.4%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

   7. Simplified 85.1%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(b \cdot 2\right)}}} \]

   if 8.0000000000000003e161 < t

   1. Initial program 95.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 100.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)}}\\ \mathbf{elif}\;t \leq 200000000000:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+161}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 4: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;\frac{x}{\mathsf{log1p}\left(\mathsf{expm1}\left(y + \left(x - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t -1.2e+70)
     (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
     (if (<= t 7e-47)
       t_1
       (if (<= t 1e-33)
         (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
         (if (<= t 7.2e-19)
           t_1
           (if (<= t 0.0038)
             (/ x (log1p (expm1 (+ y (- x (* 2.0 (* a (* y (- b c)))))))))
             (/
              x
              (+
               x
               (*
                y
                (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -1.2e+70) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 7e-47) {
		tmp = t_1;
	} else if (t <= 1e-33) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else if (t <= 7.2e-19) {
		tmp = t_1;
	} else if (t <= 0.0038) {
		tmp = x / log1p(expm1((y + (x - (2.0 * (a * (y * (b - c))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -1.2e+70) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 7e-47) {
		tmp = t_1;
	} else if (t <= 1e-33) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else if (t <= 7.2e-19) {
		tmp = t_1;
	} else if (t <= 0.0038) {
		tmp = x / Math.log1p(Math.expm1((y + (x - (2.0 * (a * (y * (b - c))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= -1.2e+70:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 7e-47:
		tmp = t_1
	elif t <= 1e-33:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	elif t <= 7.2e-19:
		tmp = t_1
	elif t <= 0.0038:
		tmp = x / math.log1p(math.expm1((y + (x - (2.0 * (a * (y * (b - c))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= -1.2e+70)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 7e-47)
		tmp = t_1;
	elseif (t <= 1e-33)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	elseif (t <= 7.2e-19)
		tmp = t_1;
	elseif (t <= 0.0038)
		tmp = Float64(x / log1p(expm1(Float64(y + Float64(x - Float64(2.0 * Float64(a * Float64(y * Float64(b - c)))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+70], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-47], t$95$1, If[LessEqual[t, 1e-33], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-19], t$95$1, If[LessEqual[t, 0.0038], N[(x / N[Log[1 + N[(Exp[N[(y + N[(x - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.19999999999999993e70

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   if -1.19999999999999993e70 < t < 6.9999999999999996e-47 or 1.0000000000000001e-33 < t < 7.2000000000000002e-19

   1. Initial program 94.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 84.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.3%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 6.9999999999999996e-47 < t < 1.0000000000000001e-33

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 86.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 86.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 86.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 86.2%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if 7.2000000000000002e-19 < t < 0.00379999999999999999

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 64.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 64.8%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 64.8%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 64.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 64.8%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 64.8%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]
   6. Step-by-step derivation

      1. log1p-expm1-u 100.0%

         \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)\right)\right)}} \]

      2. associate-+l+ 100.0%

         \[\leadsto \frac{x}{\mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{y + \left(x + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)\right)}\right)\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \frac{x}{\mathsf{log1p}\left(\mathsf{expm1}\left(y + \left(x + \color{blue}{\left(a \cdot \left(\left(c - b\right) \cdot y\right)\right) \cdot 2}\right)\right)\right)} \]

   7. Applied egg-rr 100.0%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(y + \left(x + \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right) \cdot 2\right)\right)\right)}} \]

   if 0.00379999999999999999 < t

   1. Initial program 97.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 94.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 94.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 94.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;\frac{x}{\mathsf{log1p}\left(\mathsf{expm1}\left(y + \left(x - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 5: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.7e+68)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1.62e-121)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (if (<= t 2e+14)
       (/
        x
        (+
         x
         (*
          y
          (pow
           (exp (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a)))
           (* 2.0 b)))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.7e+68) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.62e-121) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 2e+14) {
		tmp = x / (x + (y * pow(exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.7d+68)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.62d-121) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if (t <= 2d+14) then
        tmp = x / (x + (y * (exp(((0.6666666666666666d0 / t) + ((-0.8333333333333334d0) - a))) ** (2.0d0 * b))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.7e+68) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.62e-121) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 2e+14) {
		tmp = x / (x + (y * Math.pow(Math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.7e+68:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.62e-121:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif t <= 2e+14:
		tmp = x / (x + (y * math.pow(math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.7e+68)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.62e-121)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif (t <= 2e+14)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))) ^ Float64(2.0 * b)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.7e+68)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.62e-121)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif (t <= 2e+14)
		tmp = x / (x + (y * (exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))) ^ (2.0 * b))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.7e+68], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.62e-121], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+14], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(2.0 * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.69999999999999998e68

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   if -3.69999999999999998e68 < t < 1.6199999999999999e-121

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 89.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 85.7%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 1.6199999999999999e-121 < t < 2e14

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 72.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 72.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   5. Taylor expanded in y around 0 72.3%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   6. Step-by-step derivation

      1. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

      2. associate--r+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      3. sub-neg 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \left(-a\right)\right)}}} \]

      4. mul-1-neg 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{-1 \cdot a}\right)}} \]

      5. +-commutative 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      6. associate--l+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      7. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(b \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)\right)}}} \]

      8. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      9. associate--l+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      10. +-commutative 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + -1 \cdot a\right)}}} \]

      11. mul-1-neg 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{\left(-a\right)}\right)}} \]

      12. sub-neg 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      13. associate--r+ 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

   7. Simplified 79.8%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(b \cdot 2\right)}}} \]

   if 2e14 < t

   1. Initial program 97.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 95.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 95.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 6: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.05e-190)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
   (if (<= t 3.6e-121)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (if (<= t 1.26e+14)
       (/
        x
        (+
         x
         (*
          y
          (pow
           (exp (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a)))
           (* 2.0 b)))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.05e-190) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 3.6e-121) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 1.26e+14) {
		tmp = x / (x + (y * pow(exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= 1.05d-190) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 3.6d-121) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if (t <= 1.26d+14) then
        tmp = x / (x + (y * (exp(((0.6666666666666666d0 / t) + ((-0.8333333333333334d0) - a))) ** (2.0d0 * b))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.05e-190) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 3.6e-121) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 1.26e+14) {
		tmp = x / (x + (y * Math.pow(Math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.05e-190:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 3.6e-121:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif t <= 1.26e+14:
		tmp = x / (x + (y * math.pow(math.exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))), (2.0 * b))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.05e-190)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 3.6e-121)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif (t <= 1.26e+14)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))) ^ Float64(2.0 * b)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1.05e-190)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 3.6e-121)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif (t <= 1.26e+14)
		tmp = x / (x + (y * (exp(((0.6666666666666666 / t) + (-0.8333333333333334 - a))) ^ (2.0 * b))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.05e-190], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-121], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.26e+14], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(2.0 * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < 1.04999999999999996e-190

   1. Initial program 91.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 92.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   if 1.04999999999999996e-190 < t < 3.59999999999999984e-121

   1. Initial program 95.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 65.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 95.2%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 3.59999999999999984e-121 < t < 1.26e14

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 72.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 72.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   5. Taylor expanded in y around 0 72.3%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   6. Step-by-step derivation

      1. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

      2. associate--r+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      3. sub-neg 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \left(-a\right)\right)}}} \]

      4. mul-1-neg 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{-1 \cdot a}\right)}} \]

      5. +-commutative 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      6. associate--l+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      7. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(b \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)\right)}}} \]

      8. associate-*r* 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(2 \cdot b\right) \cdot \left(\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right) - 0.8333333333333334\right)}}} \]

      9. associate--l+ 72.3%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(-1 \cdot a + \left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right)\right)}}} \]

      10. +-commutative 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + -1 \cdot a\right)}}} \]

      11. mul-1-neg 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) + \color{blue}{\left(-a\right)}\right)}} \]

      12. sub-neg 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}}} \]

      13. associate--r+ 72.3%

          \[\leadsto \frac{x}{x + y \cdot e^{\left(2 \cdot b\right) \cdot \color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)}}} \]

   7. Simplified 79.8%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(b \cdot 2\right)}}} \]

   if 1.26e14 < t

   1. Initial program 97.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 95.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 95.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 95.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.05 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)}\right)}^{\left(2 \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 7: 76.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ t_3 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667))))))
        (t_2 (/ x (+ x (* y (exp (* 2.0 (* a (- c b))))))))
        (t_3 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t -3.7e+68)
     t_2
     (if (<= t 5e-47)
       t_3
       (if (<= t 9.5e-34)
         t_1
         (if (<= t 1.45e-19) t_3 (if (<= t 3.1e+16) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	double t_2 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	double t_3 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -3.7e+68) {
		tmp = t_2;
	} else if (t <= 5e-47) {
		tmp = t_3;
	} else if (t <= 9.5e-34) {
		tmp = t_1;
	} else if (t <= 1.45e-19) {
		tmp = t_3;
	} else if (t <= 3.1e+16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    t_2 = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    t_3 = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= (-3.7d+68)) then
        tmp = t_2
    else if (t <= 5d-47) then
        tmp = t_3
    else if (t <= 9.5d-34) then
        tmp = t_1
    else if (t <= 1.45d-19) then
        tmp = t_3
    else if (t <= 3.1d+16) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	double t_2 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double t_3 = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -3.7e+68) {
		tmp = t_2;
	} else if (t <= 5e-47) {
		tmp = t_3;
	} else if (t <= 9.5e-34) {
		tmp = t_1;
	} else if (t <= 1.45e-19) {
		tmp = t_3;
	} else if (t <= 3.1e+16) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	t_2 = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	t_3 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= -3.7e+68:
		tmp = t_2
	elif t <= 5e-47:
		tmp = t_3
	elif t <= 9.5e-34:
		tmp = t_1
	elif t <= 1.45e-19:
		tmp = t_3
	elif t <= 3.1e+16:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))))
	t_3 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= -3.7e+68)
		tmp = t_2;
	elseif (t <= 5e-47)
		tmp = t_3;
	elseif (t <= 9.5e-34)
		tmp = t_1;
	elseif (t <= 1.45e-19)
		tmp = t_3;
	elseif (t <= 3.1e+16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	t_2 = x / (x + (y * exp((2.0 * (a * (c - b))))));
	t_3 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= -3.7e+68)
		tmp = t_2;
	elseif (t <= 5e-47)
		tmp = t_3;
	elseif (t <= 9.5e-34)
		tmp = t_1;
	elseif (t <= 1.45e-19)
		tmp = t_3;
	elseif (t <= 3.1e+16)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+68], t$95$2, If[LessEqual[t, 5e-47], t$95$3, If[LessEqual[t, 9.5e-34], t$95$1, If[LessEqual[t, 1.45e-19], t$95$3, If[LessEqual[t, 3.1e+16], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999998e68 or 1.45e-19 < t < 3.1e16

   1. Initial program 95.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   if -3.69999999999999998e68 < t < 5.00000000000000011e-47 or 9.49999999999999985e-34 < t < 1.45e-19

   1. Initial program 94.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 85.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 83.0%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 5.00000000000000011e-47 < t < 9.49999999999999985e-34 or 3.1e16 < t

   1. Initial program 97.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 94.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 94.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 94.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 83.6%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 8: 82.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -3.8e+68)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 4e-47)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.8e+68) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-47) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-3.8d+68)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4d-47) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -3.8e+68) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-47) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -3.8e+68:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4e-47:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -3.8e+68)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4e-47)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -3.8e+68)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4e-47)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -3.8e+68], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-47], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000001e68

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   if -3.8000000000000001e68 < t < 3.9999999999999999e-47

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 84.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.0%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 3.9999999999999999e-47 < t

   1. Initial program 98.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 89.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 89.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 89.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 9: 75.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+69} \lor \neg \left(t \leq 3 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.65e+69) (not (<= t 3e-47)))
   (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.65e+69) || !(t <= 3e-47)) {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.65d+69)) .or. (.not. (t <= 3d-47))) then
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    else
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.65e+69) || !(t <= 3e-47)) {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.65e+69) or not (t <= 3e-47):
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.65e+69) || !(t <= 3e-47))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.65e+69) || ~((t <= 3e-47)))
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.65e+69], N[Not[LessEqual[t, 3e-47]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6499999999999999e69 or 3.00000000000000017e-47 < t

   1. Initial program 97.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 90.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 90.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 90.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 79.3%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -1.6499999999999999e69 < t < 3.00000000000000017e-47

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 84.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.0%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+69} \lor \neg \left(t \leq 3 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \end{array} \]

Alternative 10: 59.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq -1 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 0.0002:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot b\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) -1e+27)
   (/ x (* y (exp (* (- c b) 1.6666666666666667))))
   (if (<= (- b c) 0.0002)
     (/
      x
      (+
       x
       (-
        y
        (*
         2.0
         (* (* y b) (- a (+ (/ 0.6666666666666666 t) -0.8333333333333334)))))))
     (if (<= (- b c) 2e+147)
       1.0
       (if (<= (- b c) 1e+254)
         (/ x (+ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c)))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -1e+27) {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	} else if ((b - c) <= 0.0002) {
		tmp = x / (x + (y - (2.0 * ((y * b) * (a - ((0.6666666666666666 / t) + -0.8333333333333334))))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= (-1d+27)) then
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    else if ((b - c) <= 0.0002d0) then
        tmp = x / (x + (y - (2.0d0 * ((y * b) * (a - ((0.6666666666666666d0 / t) + (-0.8333333333333334d0)))))))
    else if ((b - c) <= 2d+147) then
        tmp = 1.0d0
    else if ((b - c) <= 1d+254) then
        tmp = x / (x + (y + (1.3333333333333333d0 * (y / (t / (b - c))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -1e+27) {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	} else if ((b - c) <= 0.0002) {
		tmp = x / (x + (y - (2.0 * ((y * b) * (a - ((0.6666666666666666 / t) + -0.8333333333333334))))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= -1e+27:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	elif (b - c) <= 0.0002:
		tmp = x / (x + (y - (2.0 * ((y * b) * (a - ((0.6666666666666666 / t) + -0.8333333333333334))))))
	elif (b - c) <= 2e+147:
		tmp = 1.0
	elif (b - c) <= 1e+254:
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= -1e+27)
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	elseif (Float64(b - c) <= 0.0002)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(y * b) * Float64(a - Float64(Float64(0.6666666666666666 / t) + -0.8333333333333334)))))));
	elseif (Float64(b - c) <= 2e+147)
		tmp = 1.0;
	elseif (Float64(b - c) <= 1e+254)
		tmp = Float64(x / Float64(x + Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= -1e+27)
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	elseif ((b - c) <= 0.0002)
		tmp = x / (x + (y - (2.0 * ((y * b) * (a - ((0.6666666666666666 / t) + -0.8333333333333334))))));
	elseif ((b - c) <= 2e+147)
		tmp = 1.0;
	elseif ((b - c) <= 1e+254)
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], -1e+27], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 0.0002], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(y * b), $MachinePrecision] * N[(a - N[(N[(0.6666666666666666 / t), $MachinePrecision] + -0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 2e+147], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 1e+254], N[(x / N[(x + N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 b c) < -1e27

   1. Initial program 94.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 78.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 78.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 78.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 74.5%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   6. Taylor expanded in x around 0 74.5%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -1e27 < (-.f64 b c) < 2.0000000000000001e-4

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 67.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 67.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 67.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 67.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   5. Taylor expanded in b around 0 57.9%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(b \cdot \left(y \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(b \cdot y\right) \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}\right)} \]

      2. associate--r+ 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \color{blue}{\left(\left(0.6666666666666666 \cdot \frac{1}{t} - 0.8333333333333334\right) - a\right)}\right)\right)} \]

      3. sub-neg 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \left(\color{blue}{\left(0.6666666666666666 \cdot \frac{1}{t} + \left(-0.8333333333333334\right)\right)} - a\right)\right)\right)} \]

      4. associate-*r/ 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \left(\left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} + \left(-0.8333333333333334\right)\right) - a\right)\right)\right)} \]

      5. metadata-eval 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \left(\left(\frac{\color{blue}{0.6666666666666666}}{t} + \left(-0.8333333333333334\right)\right) - a\right)\right)\right)} \]

      6. metadata-eval 59.3%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \left(\left(\frac{0.6666666666666666}{t} + \color{blue}{-0.8333333333333334}\right) - a\right)\right)\right)} \]

   7. Simplified 59.3%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(b \cdot y\right) \cdot \left(\left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right) - a\right)\right)\right)}} \]

   if 2.0000000000000001e-4 < (-.f64 b c) < 2e147 or 9.9999999999999994e253 < (-.f64 b c)

   1. Initial program 95.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 63.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.8%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.8%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.8%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.8%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{1} \]

   if 2e147 < (-.f64 b c) < 9.9999999999999994e253

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 44.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.1%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in t around inf 54.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}\right)}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   6. Simplified 64.3%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq -1 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 0.0002:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot b\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 62.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3e+197)
   (/ x (+ (+ x y) (* 2.0 (* a (* y (- c b))))))
   (/ x (+ x (* y (exp (* (- c b) 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3e+197) {
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	} else {
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-3d+197)) then
        tmp = x / ((x + y) + (2.0d0 * (a * (y * (c - b)))))
    else
        tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3e+197) {
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	} else {
		tmp = x / (x + (y * Math.exp(((c - b) * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3e+197:
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))))
	else:
		tmp = x / (x + (y * math.exp(((c - b) * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3e+197)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(2.0 * Float64(a * Float64(y * Float64(c - b))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3e+197)
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	else
		tmp = x / (x + (y * exp(((c - b) * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3e+197], N[(x / N[(N[(x + y), $MachinePrecision] + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000002e197

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 57.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 75.8%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 75.8%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 75.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 75.8%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   if -3.0000000000000002e197 < y

   1. Initial program 95.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 74.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 74.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 74.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 67.0%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 12: 52.6% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq -5 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b - c \leq 10^{+189}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) -2e+63)
   (/ x (* y (+ 1.0 (* (- c b) (* 2.0 a)))))
   (if (<= (- b c) -5e+37)
     1.0
     (if (<= (- b c) 5e-90)
       (/ x (+ (+ x y) (* 2.0 (* y (* a c)))))
       (if (<= (- b c) 1e+189)
         1.0
         (if (<= (- b c) 2e+214)
           (/ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c))))))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e+63) {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	} else if ((b - c) <= -5e+37) {
		tmp = 1.0;
	} else if ((b - c) <= 5e-90) {
		tmp = x / ((x + y) + (2.0 * (y * (a * c))));
	} else if ((b - c) <= 1e+189) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+214) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= (-2d+63)) then
        tmp = x / (y * (1.0d0 + ((c - b) * (2.0d0 * a))))
    else if ((b - c) <= (-5d+37)) then
        tmp = 1.0d0
    else if ((b - c) <= 5d-90) then
        tmp = x / ((x + y) + (2.0d0 * (y * (a * c))))
    else if ((b - c) <= 1d+189) then
        tmp = 1.0d0
    else if ((b - c) <= 2d+214) then
        tmp = x / (y + (1.3333333333333333d0 * (y / (t / (b - c)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e+63) {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	} else if ((b - c) <= -5e+37) {
		tmp = 1.0;
	} else if ((b - c) <= 5e-90) {
		tmp = x / ((x + y) + (2.0 * (y * (a * c))));
	} else if ((b - c) <= 1e+189) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+214) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= -2e+63:
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))))
	elif (b - c) <= -5e+37:
		tmp = 1.0
	elif (b - c) <= 5e-90:
		tmp = x / ((x + y) + (2.0 * (y * (a * c))))
	elif (b - c) <= 1e+189:
		tmp = 1.0
	elif (b - c) <= 2e+214:
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= -2e+63)
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a)))));
	elseif (Float64(b - c) <= -5e+37)
		tmp = 1.0;
	elseif (Float64(b - c) <= 5e-90)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(2.0 * Float64(y * Float64(a * c)))));
	elseif (Float64(b - c) <= 1e+189)
		tmp = 1.0;
	elseif (Float64(b - c) <= 2e+214)
		tmp = Float64(x / Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= -2e+63)
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	elseif ((b - c) <= -5e+37)
		tmp = 1.0;
	elseif ((b - c) <= 5e-90)
		tmp = x / ((x + y) + (2.0 * (y * (a * c))));
	elseif ((b - c) <= 1e+189)
		tmp = 1.0;
	elseif ((b - c) <= 2e+214)
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], -2e+63], N[(x / N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], -5e+37], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 5e-90], N[(x / N[(N[(x + y), $MachinePrecision] + N[(2.0 * N[(y * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 1e+189], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 2e+214], N[(x / N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 b c) < -2.00000000000000012e63

   1. Initial program 95.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 65.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 49.0%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 49.0%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 49.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 49.0%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 49.0%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in y around inf 40.8%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto \frac{x}{y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   8. Simplified 40.8%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]

   if -2.00000000000000012e63 < (-.f64 b c) < -4.99999999999999989e37 or 5.00000000000000019e-90 < (-.f64 b c) < 1e189 or 1.9999999999999999e214 < (-.f64 b c)

   1. Initial program 94.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 58.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 38.9%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 38.9%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 38.9%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 38.9%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 38.9%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 65.6%

      \[\leadsto \color{blue}{1} \]

   if -4.99999999999999989e37 < (-.f64 b c) < 5.00000000000000019e-90

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 76.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 58.3%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 58.3%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 58.3%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 58.3%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 58.3%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in c around inf 58.4%

      \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \color{blue}{\left(a \cdot \left(c \cdot y\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot y\right)}} \]

   8. Simplified 58.5%

      \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \color{blue}{\left(\left(a \cdot c\right) \cdot y\right)}} \]

   if 1e189 < (-.f64 b c) < 1.9999999999999999e214

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 43.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 86.2%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in x around 0 86.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   5. Taylor expanded in t around inf 72.3%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   7. Simplified 86.2%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq -5 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(y \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b - c \leq 10^{+189}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 53.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) -2e+201)
   (/ x (+ (+ x y) (* 2.0 (* a (* y (- c b))))))
   (if (<= (- b c) 5e-90)
     (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
     (if (<= (- b c) 2e+147)
       1.0
       (if (<= (- b c) 1e+254)
         (/ x (+ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c)))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e+201) {
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	} else if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= (-2d+201)) then
        tmp = x / ((x + y) + (2.0d0 * (a * (y * (c - b)))))
    else if ((b - c) <= 5d-90) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if ((b - c) <= 2d+147) then
        tmp = 1.0d0
    else if ((b - c) <= 1d+254) then
        tmp = x / (x + (y + (1.3333333333333333d0 * (y / (t / (b - c))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e+201) {
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	} else if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= -2e+201:
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))))
	elif (b - c) <= 5e-90:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif (b - c) <= 2e+147:
		tmp = 1.0
	elif (b - c) <= 1e+254:
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= -2e+201)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(2.0 * Float64(a * Float64(y * Float64(c - b))))));
	elseif (Float64(b - c) <= 5e-90)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (Float64(b - c) <= 2e+147)
		tmp = 1.0;
	elseif (Float64(b - c) <= 1e+254)
		tmp = Float64(x / Float64(x + Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= -2e+201)
		tmp = x / ((x + y) + (2.0 * (a * (y * (c - b)))));
	elseif ((b - c) <= 5e-90)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif ((b - c) <= 2e+147)
		tmp = 1.0;
	elseif ((b - c) <= 1e+254)
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], -2e+201], N[(x / N[(N[(x + y), $MachinePrecision] + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 5e-90], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 2e+147], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 1e+254], N[(x / N[(x + N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 b c) < -2.00000000000000008e201

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 60.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 63.3%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 63.3%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 63.3%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 63.3%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 63.3%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   if -2.00000000000000008e201 < (-.f64 b c) < 5.00000000000000019e-90

   1. Initial program 97.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 70.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 51.8%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*r* 51.8%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   5. Simplified 51.8%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]

   if 5.00000000000000019e-90 < (-.f64 b c) < 2e147 or 9.9999999999999994e253 < (-.f64 b c)

   1. Initial program 96.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 63.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.4%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.4%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.4%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.4%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 69.5%

      \[\leadsto \color{blue}{1} \]

   if 2e147 < (-.f64 b c) < 9.9999999999999994e253

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 44.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.1%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in t around inf 54.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}\right)}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   6. Simplified 64.3%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{+201}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 53.6% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) 5e-90)
   (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
   (if (<= (- b c) 2e+147)
     1.0
     (if (<= (- b c) 1e+254)
       (/ x (+ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c)))))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= 5d-90) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if ((b - c) <= 2d+147) then
        tmp = 1.0d0
    else if ((b - c) <= 1d+254) then
        tmp = x / (x + (y + (1.3333333333333333d0 * (y / (t / (b - c))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= 5e-90:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif (b - c) <= 2e+147:
		tmp = 1.0
	elif (b - c) <= 1e+254:
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= 5e-90)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (Float64(b - c) <= 2e+147)
		tmp = 1.0;
	elseif (Float64(b - c) <= 1e+254)
		tmp = Float64(x / Float64(x + Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= 5e-90)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif ((b - c) <= 2e+147)
		tmp = 1.0;
	elseif ((b - c) <= 1e+254)
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], 5e-90], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 2e+147], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 1e+254], N[(x / N[(x + N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b c) < 5.00000000000000019e-90

   1. Initial program 96.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 68.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 51.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   5. Simplified 51.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]

   if 5.00000000000000019e-90 < (-.f64 b c) < 2e147 or 9.9999999999999994e253 < (-.f64 b c)

   1. Initial program 96.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 63.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.4%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.4%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.4%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.4%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 69.5%

      \[\leadsto \color{blue}{1} \]

   if 2e147 < (-.f64 b c) < 9.9999999999999994e253

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 44.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.1%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in t around inf 54.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}\right)}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   6. Simplified 64.3%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 50.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq 0.0002:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot c\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) 0.0002)
   (/
    x
    (-
     x
     (*
      y
      (-
       -1.0
       (* 2.0 (* (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t))) c))))))
   (if (<= (- b c) 2e+147)
     1.0
     (if (<= (- b c) 1e+254)
       (/ x (+ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c)))))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 0.0002) {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((0.8333333333333334 + (a - (0.6666666666666666 / t))) * c)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= 0.0002d0) then
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * ((0.8333333333333334d0 + (a - (0.6666666666666666d0 / t))) * c)))))
    else if ((b - c) <= 2d+147) then
        tmp = 1.0d0
    else if ((b - c) <= 1d+254) then
        tmp = x / (x + (y + (1.3333333333333333d0 * (y / (t / (b - c))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 0.0002) {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((0.8333333333333334 + (a - (0.6666666666666666 / t))) * c)))));
	} else if ((b - c) <= 2e+147) {
		tmp = 1.0;
	} else if ((b - c) <= 1e+254) {
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= 0.0002:
		tmp = x / (x - (y * (-1.0 - (2.0 * ((0.8333333333333334 + (a - (0.6666666666666666 / t))) * c)))))
	elif (b - c) <= 2e+147:
		tmp = 1.0
	elif (b - c) <= 1e+254:
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= 0.0002)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))) * c))))));
	elseif (Float64(b - c) <= 2e+147)
		tmp = 1.0;
	elseif (Float64(b - c) <= 1e+254)
		tmp = Float64(x / Float64(x + Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= 0.0002)
		tmp = x / (x - (y * (-1.0 - (2.0 * ((0.8333333333333334 + (a - (0.6666666666666666 / t))) * c)))));
	elseif ((b - c) <= 2e+147)
		tmp = 1.0;
	elseif ((b - c) <= 1e+254)
		tmp = x / (x + (y + (1.3333333333333333 * (y / (t / (b - c))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], 0.0002], N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 2e+147], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 1e+254], N[(x / N[(x + N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b c) < 2.0000000000000001e-4

   1. Initial program 97.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 71.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 71.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 71.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 71.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 71.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 51.7%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. +-commutative 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      2. associate-*r/ 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      3. metadata-eval 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      4. unsub-neg 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \color{blue}{\left(\left(a + 0.8333333333333334\right) + \left(-\frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

      5. +-commutative 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(\color{blue}{\left(0.8333333333333334 + a\right)} + \left(-\frac{0.6666666666666666}{t}\right)\right)\right)\right)} \]

      6. associate-+l+ 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \color{blue}{\left(0.8333333333333334 + \left(a + \left(-\frac{0.6666666666666666}{t}\right)\right)\right)}\right)\right)} \]

      7. remove-double-neg 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(\color{blue}{\left(-\left(-a\right)\right)} + \left(-\frac{0.6666666666666666}{t}\right)\right)\right)\right)\right)} \]

      8. mul-1-neg 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(\left(-\color{blue}{-1 \cdot a}\right) + \left(-\frac{0.6666666666666666}{t}\right)\right)\right)\right)\right)} \]

      9. distribute-neg-in 51.7%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \color{blue}{\left(-\left(-1 \cdot a + \frac{0.6666666666666666}{t}\right)\right)}\right)\right)\right)} \]

      10. metadata-eval 51.7%

          \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(-\left(-1 \cdot a + \frac{\color{blue}{0.6666666666666666 \cdot 1}}{t}\right)\right)\right)\right)\right)} \]

      11. associate-*r/ 51.7%

          \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(-\left(-1 \cdot a + \color{blue}{0.6666666666666666 \cdot \frac{1}{t}}\right)\right)\right)\right)\right)} \]

      12. sub-neg 51.7%

          \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \color{blue}{\left(0.8333333333333334 - \left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)\right)} \]

      13. sub-neg 51.7%

          \[\leadsto \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \color{blue}{\left(0.8333333333333334 + \left(-\left(-1 \cdot a + 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)}\right)\right)} \]

   7. Simplified 51.7%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]

   if 2.0000000000000001e-4 < (-.f64 b c) < 2e147 or 9.9999999999999994e253 < (-.f64 b c)

   1. Initial program 95.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 63.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.8%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.8%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.8%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.8%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.8%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 74.6%

      \[\leadsto \color{blue}{1} \]

   if 2e147 < (-.f64 b c) < 9.9999999999999994e253

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 44.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 82.1%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in t around inf 54.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}\right)}} \]
   5. Step-by-step derivation

      1. associate-/l* 46.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   6. Simplified 64.3%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq 0.0002:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot c\right)\right)}\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 10^{+254}:\\ \;\;\;\;\frac{x}{x + \left(y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16: 55.9% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 10^{+189}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) 5e-90)
   (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
   (if (<= (- b c) 1e+189)
     1.0
     (if (<= (- b c) 2e+214)
       (/ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c))))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 1e+189) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+214) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= 5d-90) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if ((b - c) <= 1d+189) then
        tmp = 1.0d0
    else if ((b - c) <= 2d+214) then
        tmp = x / (y + (1.3333333333333333d0 * (y / (t / (b - c)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= 5e-90) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if ((b - c) <= 1e+189) {
		tmp = 1.0;
	} else if ((b - c) <= 2e+214) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= 5e-90:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif (b - c) <= 1e+189:
		tmp = 1.0
	elif (b - c) <= 2e+214:
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= 5e-90)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (Float64(b - c) <= 1e+189)
		tmp = 1.0;
	elseif (Float64(b - c) <= 2e+214)
		tmp = Float64(x / Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= 5e-90)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif ((b - c) <= 1e+189)
		tmp = 1.0;
	elseif ((b - c) <= 2e+214)
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], 5e-90], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 1e+189], 1.0, If[LessEqual[N[(b - c), $MachinePrecision], 2e+214], N[(x / N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b c) < 5.00000000000000019e-90

   1. Initial program 96.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 68.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 51.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*r* 51.2%

         \[\leadsto \frac{x}{x + y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   5. Simplified 51.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]

   if 5.00000000000000019e-90 < (-.f64 b c) < 1e189 or 1.9999999999999999e214 < (-.f64 b c)

   1. Initial program 94.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 59.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 39.9%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 39.9%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 39.9%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 39.9%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 39.9%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{1} \]

   if 1e189 < (-.f64 b c) < 1.9999999999999999e214

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 43.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 86.2%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in x around 0 86.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   5. Taylor expanded in t around inf 72.3%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.2%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   7. Simplified 86.2%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq 5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b - c \leq 10^{+189}:\\ \;\;\;\;1\\ \mathbf{elif}\;b - c \leq 2 \cdot 10^{+214}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 48.5% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y}\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{a}}{y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x y))))
   (if (<= c -1.65e-86)
     1.0
     (if (<= c -3.4e-191)
       t_1
       (if (<= c 8.5e-308)
         1.0
         (if (<= c 9.2e-173)
           t_1
           (if (<= c 2.35e+75) 1.0 (* 0.5 (/ (/ x a) (* y c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + y);
	double tmp;
	if (c <= -1.65e-86) {
		tmp = 1.0;
	} else if (c <= -3.4e-191) {
		tmp = t_1;
	} else if (c <= 8.5e-308) {
		tmp = 1.0;
	} else if (c <= 9.2e-173) {
		tmp = t_1;
	} else if (c <= 2.35e+75) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * ((x / a) / (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + y)
    if (c <= (-1.65d-86)) then
        tmp = 1.0d0
    else if (c <= (-3.4d-191)) then
        tmp = t_1
    else if (c <= 8.5d-308) then
        tmp = 1.0d0
    else if (c <= 9.2d-173) then
        tmp = t_1
    else if (c <= 2.35d+75) then
        tmp = 1.0d0
    else
        tmp = 0.5d0 * ((x / a) / (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + y);
	double tmp;
	if (c <= -1.65e-86) {
		tmp = 1.0;
	} else if (c <= -3.4e-191) {
		tmp = t_1;
	} else if (c <= 8.5e-308) {
		tmp = 1.0;
	} else if (c <= 9.2e-173) {
		tmp = t_1;
	} else if (c <= 2.35e+75) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * ((x / a) / (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + y)
	tmp = 0
	if c <= -1.65e-86:
		tmp = 1.0
	elif c <= -3.4e-191:
		tmp = t_1
	elif c <= 8.5e-308:
		tmp = 1.0
	elif c <= 9.2e-173:
		tmp = t_1
	elif c <= 2.35e+75:
		tmp = 1.0
	else:
		tmp = 0.5 * ((x / a) / (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + y))
	tmp = 0.0
	if (c <= -1.65e-86)
		tmp = 1.0;
	elseif (c <= -3.4e-191)
		tmp = t_1;
	elseif (c <= 8.5e-308)
		tmp = 1.0;
	elseif (c <= 9.2e-173)
		tmp = t_1;
	elseif (c <= 2.35e+75)
		tmp = 1.0;
	else
		tmp = Float64(0.5 * Float64(Float64(x / a) / Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + y);
	tmp = 0.0;
	if (c <= -1.65e-86)
		tmp = 1.0;
	elseif (c <= -3.4e-191)
		tmp = t_1;
	elseif (c <= 8.5e-308)
		tmp = 1.0;
	elseif (c <= 9.2e-173)
		tmp = t_1;
	elseif (c <= 2.35e+75)
		tmp = 1.0;
	else
		tmp = 0.5 * ((x / a) / (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e-86], 1.0, If[LessEqual[c, -3.4e-191], t$95$1, If[LessEqual[c, 8.5e-308], 1.0, If[LessEqual[c, 9.2e-173], t$95$1, If[LessEqual[c, 2.35e+75], 1.0, N[(0.5 * N[(N[(x / a), $MachinePrecision] / N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.64999999999999993e-86 or -3.39999999999999994e-191 < c < 8.49999999999999972e-308 or 9.19999999999999951e-173 < c < 2.34999999999999992e75

   1. Initial program 96.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 59.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 40.4%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 40.4%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 40.4%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 40.4%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 40.4%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 55.7%

      \[\leadsto \color{blue}{1} \]

   if -1.64999999999999993e-86 < c < -3.39999999999999994e-191 or 8.49999999999999972e-308 < c < 9.19999999999999951e-173

   1. Initial program 98.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 78.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 58.7%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   4. Step-by-step derivation

      1. +-commutative 58.7%

         \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   5. Simplified 58.7%

      \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   if 2.34999999999999992e75 < c

   1. Initial program 92.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 67.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 57.7%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 57.7%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 57.7%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 57.7%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 57.7%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in a around inf 53.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{a \cdot \left(y \cdot \left(c - b\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 53.5%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{a \cdot \left(y \cdot \left(c - b\right)\right)}} \]

      2. associate-*r* 42.3%

         \[\leadsto \frac{0.5 \cdot x}{\color{blue}{\left(a \cdot y\right) \cdot \left(c - b\right)}} \]

   8. Simplified 42.3%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{\left(a \cdot y\right) \cdot \left(c - b\right)}} \]

   9. Taylor expanded in c around inf 51.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{a \cdot \left(c \cdot y\right)}} \]
   10. Step-by-step derivation

       1. associate-/r* 45.6%

          \[\leadsto 0.5 \cdot \color{blue}{\frac{\frac{x}{a}}{c \cdot y}} \]

   11. Simplified 45.6%

       \[\leadsto \color{blue}{0.5 \cdot \frac{\frac{x}{a}}{c \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{+75}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{a}}{y \cdot c}\\ \end{array} \]

Alternative 18: 49.0% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.2 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+212}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 5.2e-36)
   1.0
   (if (<= a 1.66e+28)
     (/ x (+ y (* 1.3333333333333333 (/ y (/ t (- b c))))))
     (if (<= a 5.1e+212) 1.0 (/ x (* y (+ 1.0 (* (- c b) (* 2.0 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 5.2e-36) {
		tmp = 1.0;
	} else if (a <= 1.66e+28) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else if (a <= 5.1e+212) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 5.2d-36) then
        tmp = 1.0d0
    else if (a <= 1.66d+28) then
        tmp = x / (y + (1.3333333333333333d0 * (y / (t / (b - c)))))
    else if (a <= 5.1d+212) then
        tmp = 1.0d0
    else
        tmp = x / (y * (1.0d0 + ((c - b) * (2.0d0 * a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 5.2e-36) {
		tmp = 1.0;
	} else if (a <= 1.66e+28) {
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	} else if (a <= 5.1e+212) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 5.2e-36:
		tmp = 1.0
	elif a <= 1.66e+28:
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))))
	elif a <= 5.1e+212:
		tmp = 1.0
	else:
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 5.2e-36)
		tmp = 1.0;
	elseif (a <= 1.66e+28)
		tmp = Float64(x / Float64(y + Float64(1.3333333333333333 * Float64(y / Float64(t / Float64(b - c))))));
	elseif (a <= 5.1e+212)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 5.2e-36)
		tmp = 1.0;
	elseif (a <= 1.66e+28)
		tmp = x / (y + (1.3333333333333333 * (y / (t / (b - c)))));
	elseif (a <= 5.1e+212)
		tmp = 1.0;
	else
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 5.2e-36], 1.0, If[LessEqual[a, 1.66e+28], N[(x / N[(y + N[(1.3333333333333333 * N[(y / N[(t / N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.1e+212], 1.0, N[(x / N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < 5.2000000000000001e-36 or 1.6599999999999999e28 < a < 5.1000000000000002e212

   1. Initial program 96.9%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 61.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 47.2%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.2%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 47.2%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 47.2%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 47.2%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 51.3%

      \[\leadsto \color{blue}{1} \]

   if 5.2000000000000001e-36 < a < 1.6599999999999999e28

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 76.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 76.9%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   4. Taylor expanded in x around 0 57.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   5. Taylor expanded in t around inf 41.0%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y \cdot \left(b - c\right)}{t}}} \]
   6. Step-by-step derivation

      1. associate-/l* 45.6%

         \[\leadsto \frac{x}{y + 1.3333333333333333 \cdot \color{blue}{\frac{y}{\frac{t}{b - c}}}} \]

   7. Simplified 45.6%

      \[\leadsto \frac{x}{\color{blue}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}} \]

   if 5.1000000000000002e212 < a

   1. Initial program 90.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 87.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 49.7%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 49.7%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 49.7%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 49.7%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 49.7%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in y around inf 61.3%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto \frac{x}{y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   8. Simplified 61.3%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.2 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y + 1.3333333333333333 \cdot \frac{y}{\frac{t}{b - c}}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{+212}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \]

Alternative 19: 51.1% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 6.5e+213) 1.0 (/ x (* y (+ 1.0 (* (- c b) (* 2.0 a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 6.5e+213) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 6.5d+213) then
        tmp = 1.0d0
    else
        tmp = x / (y * (1.0d0 + ((c - b) * (2.0d0 * a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 6.5e+213) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 6.5e+213:
		tmp = 1.0
	else:
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 6.5e+213)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 6.5e+213)
		tmp = 1.0;
	else
		tmp = x / (y * (1.0 + ((c - b) * (2.0 * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 6.5e+213], 1.0, N[(x / N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.49999999999999982e213

   1. Initial program 97.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 60.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 47.0%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.0%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 47.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 47.0%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 47.0%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 48.9%

      \[\leadsto \color{blue}{1} \]

   if 6.49999999999999982e213 < a

   1. Initial program 90.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 87.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 49.7%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 49.7%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 49.7%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 49.7%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 49.7%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in y around inf 61.3%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto \frac{x}{y \cdot \left(1 + \color{blue}{\left(2 \cdot a\right) \cdot \left(c - b\right)}\right)} \]

   8. Simplified 61.3%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 + \left(2 \cdot a\right) \cdot \left(c - b\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.5 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \]

Alternative 20: 50.0% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{+227}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -0.5}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a 3.4e+227) 1.0 (/ (* x -0.5) (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.4e+227) {
		tmp = 1.0;
	} else {
		tmp = (x * -0.5) / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (a <= 3.4d+227) then
        tmp = 1.0d0
    else
        tmp = (x * (-0.5d0)) / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= 3.4e+227) {
		tmp = 1.0;
	} else {
		tmp = (x * -0.5) / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= 3.4e+227:
		tmp = 1.0
	else:
		tmp = (x * -0.5) / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= 3.4e+227)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x * -0.5) / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= 3.4e+227)
		tmp = 1.0;
	else
		tmp = (x * -0.5) / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, 3.4e+227], 1.0, N[(N[(x * -0.5), $MachinePrecision] / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 3.39999999999999989e227

   1. Initial program 97.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 61.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 47.2%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 47.2%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 47.2%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 47.2%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 47.2%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 48.5%

      \[\leadsto \color{blue}{1} \]

   if 3.39999999999999989e227 < a

   1. Initial program 88.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 85.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 49.3%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 49.3%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 49.3%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 49.3%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 49.3%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in a around inf 49.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{a \cdot \left(y \cdot \left(c - b\right)\right)}} \]
   7. Step-by-step derivation

      1. associate-*r/ 49.2%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{a \cdot \left(y \cdot \left(c - b\right)\right)}} \]

      2. associate-*r* 52.1%

         \[\leadsto \frac{0.5 \cdot x}{\color{blue}{\left(a \cdot y\right) \cdot \left(c - b\right)}} \]

   8. Simplified 52.1%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{\left(a \cdot y\right) \cdot \left(c - b\right)}} \]

   9. Taylor expanded in c around 0 43.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{x}{a \cdot \left(b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. associate-*r/ 43.0%

          \[\leadsto \color{blue}{\frac{-0.5 \cdot x}{a \cdot \left(b \cdot y\right)}} \]

       2. *-commutative 43.0%

          \[\leadsto \frac{-0.5 \cdot x}{\color{blue}{\left(b \cdot y\right) \cdot a}} \]

       3. *-commutative 43.0%

          \[\leadsto \frac{-0.5 \cdot x}{\color{blue}{\left(y \cdot b\right)} \cdot a} \]

       4. associate-*l* 57.6%

          \[\leadsto \frac{-0.5 \cdot x}{\color{blue}{y \cdot \left(b \cdot a\right)}} \]

   11. Simplified 57.6%

       \[\leadsto \color{blue}{\frac{-0.5 \cdot x}{y \cdot \left(b \cdot a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.4 \cdot 10^{+227}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -0.5}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 21: 50.2% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -2.35e+197) (/ x (+ x y)) 1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.35e+197) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-2.35d+197)) then
        tmp = x / (x + y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.35e+197) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -2.35e+197:
		tmp = x / (x + y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -2.35e+197)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -2.35e+197)
		tmp = x / (x + y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -2.35e+197], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e197

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 57.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 54.4%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   4. Step-by-step derivation

      1. +-commutative 54.4%

         \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   5. Simplified 54.4%

      \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   if -2.35e197 < y

   1. Initial program 95.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 65.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.0%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.0%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.0%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.0%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.0%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 48.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 22: 50.1% accurate, 45.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (if (<= y -2.1e+208) (/ x y) 1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.1e+208) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-2.1d+208)) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.1e+208) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -2.1e+208:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -2.1e+208)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -2.1e+208)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -2.1e+208], N[(x / y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.0999999999999998e208

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 54.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 54.6%

      \[\leadsto \frac{x}{\color{blue}{x + y}} \]
   4. Step-by-step derivation

      1. +-commutative 54.6%

         \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   5. Simplified 54.6%

      \[\leadsto \frac{x}{\color{blue}{y + x}} \]

   6. Taylor expanded in x around 0 54.6%

      \[\leadsto \color{blue}{\frac{x}{y}} \]

   if -2.0999999999999998e208 < y

   1. Initial program 95.7%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 66.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

   3. Taylor expanded in a around 0 44.5%

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-+r+ 44.5%

         \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

      2. +-commutative 44.5%

         \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

      3. *-commutative 44.5%

         \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

   5. Simplified 44.5%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

   6. Taylor expanded in x around inf 48.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 23: 51.9% accurate, 231.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 1.0)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return 1.0;
}

Python

def code(x, y, z, t, a, b, c):
	return 1.0

Julia

function code(x, y, z, t, a, b, c)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := 1.0

Derivation

1. Initial program 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

2. Taylor expanded in a around inf 64.9%

   \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(a \cdot \left(c - b\right)\right)}}} \]

3. Taylor expanded in a around 0 47.5%

   \[\leadsto \frac{x}{\color{blue}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
4. Step-by-step derivation

   1. associate-+r+ 47.5%

      \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}} \]

   2. +-commutative 47.5%

      \[\leadsto \frac{x}{\color{blue}{\left(y + x\right)} + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)} \]

   3. *-commutative 47.5%

      \[\leadsto \frac{x}{\left(y + x\right) + 2 \cdot \left(a \cdot \color{blue}{\left(\left(c - b\right) \cdot y\right)}\right)} \]

5. Simplified 47.5%

   \[\leadsto \frac{x}{\color{blue}{\left(y + x\right) + 2 \cdot \left(a \cdot \left(\left(c - b\right) \cdot y\right)\right)}} \]

6. Taylor expanded in x around inf 46.3%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 46.3%

   \[\leadsto 1 \]

Developer target: 95.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t_1 \cdot \left(\left(3 \cdot t\right) \cdot t_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (- a (/ 5.0 6.0))))
   (if (< t -2.118326644891581e-50)
     (/
      x
      (+
       x
       (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b)))))))
     (if (< t 5.196588770651547e-123)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/
             (-
              (* t_1 (* (* 3.0 t) t_2))
              (*
               (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)
               (* t_2 (* (- b c) t))))
             (* (* (* t t) 3.0) t_2)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ t_1 t)
             (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * sqrt((t + a))
    t_2 = a - (5.0d0 / 6.0d0)
    if (t < (-2.118326644891581d-50)) then
        tmp = x / (x + (y * exp((2.0d0 * (((a * c) + (0.8333333333333334d0 * c)) - (a * b))))))
    else if (t < 5.196588770651547d-123) then
        tmp = x / (x + (y * exp((2.0d0 * (((t_1 * ((3.0d0 * t) * t_2)) - (((((5.0d0 / 6.0d0) + a) * (3.0d0 * t)) - 2.0d0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0d0) * t_2))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((t_1 / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * Math.sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * Math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * Math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = a - (5.0 / 6.0)
	tmp = 0
	if t < -2.118326644891581e-50:
		tmp = x / (x + (y * math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))))
	elif t < 5.196588770651547e-123:
		tmp = x / (x + (y * math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(a - Float64(5.0 / 6.0))
	tmp = 0.0
	if (t < -2.118326644891581e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(a * c) + Float64(0.8333333333333334 * c)) - Float64(a * b)))))));
	elseif (t < 5.196588770651547e-123)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(t_1 * Float64(Float64(3.0 * t) * t_2)) - Float64(Float64(Float64(Float64(Float64(5.0 / 6.0) + a) * Float64(3.0 * t)) - 2.0) * Float64(t_2 * Float64(Float64(b - c) * t)))) / Float64(Float64(Float64(t * t) * 3.0) * t_2)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_1 / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = a - (5.0 / 6.0);
	tmp = 0.0;
	if (t < -2.118326644891581e-50)
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	elseif (t < 5.196588770651547e-123)
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -2.118326644891581e-50], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(a * c), $MachinePrecision] + N[(0.8333333333333334 * c), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[t, 5.196588770651547e-123], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(t$95$1 * N[(N[(3.0 * t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(5.0 / 6.0), $MachinePrecision] + a), $MachinePrecision] * N[(3.0 * t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] * N[(t$95$2 * N[(N[(b - c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * t), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$1 / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))